50/65 Additive Inverse :
The additive inverse of 50/65 is -50/65.
This means that when we add 50/65 and -50/65, the result is zero:
50/65 + (-50/65) = 0
Additive Inverse of a Fraction
For fractions, the additive inverse is found by negating the numerator or denominator, but not both. In this case:
- Original fraction: 50/65
- Additive inverse: -50/65
To verify: 50/65 + (-50/65) = 0
Extended Mathematical Exploration of 50/65
Let's explore various mathematical operations and concepts related to 50/65 and its additive inverse -50/65.
Basic Operations and Properties
- Square of 50/65: 0.59171597633136
- Cube of 50/65: 0.45516613563951
- Square root of |50/65|: 0.87705801930703
- Reciprocal of 50/65: 1.3
- Double of 50/65: 1.5384615384615
- Half of 50/65: 0.38461538461538
- Absolute value of 50/65: 0.76923076923077
Trigonometric Functions
- Sine of 50/65: 0.69558279374803
- Cosine of 50/65: 0.71844594580364
- Tangent of 50/65: 0.96817693496756
Exponential and Logarithmic Functions
- e^50/65: 2.1581055339484
- Natural log of 50/65: -0.26236426446749
Floor and Ceiling Functions
- Floor of 50/65: 0
- Ceiling of 50/65: 1
Interesting Properties and Relationships
- The sum of 50/65 and its additive inverse (-50/65) is always 0.
- The product of 50/65 and its additive inverse is: -2500
- The average of 50/65 and its additive inverse is always 0.
- The distance between 50/65 and its additive inverse on a number line is: 100
Applications in Algebra
Consider the equation: x + 50/65 = 0
The solution to this equation is x = -50/65, which is the additive inverse of 50/65.
Graphical Representation
On a coordinate plane:
- The point (50/65, 0) is reflected across the y-axis to (-50/65, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 50/65 and Its Additive Inverse
Consider the alternating series: 50/65 + (-50/65) + 50/65 + (-50/65) + ...
The sum of this series oscillates between 0 and 50/65, never converging unless 50/65 is 0.
In Number Theory
For integer values:
- If 50/65 is even, its additive inverse is also even.
- If 50/65 is odd, its additive inverse is also odd.
- The sum of the digits of 50/65 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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